Thanks for the responses.
I use bitcoin core to select the inputs, basically the bitcoin-cli.
Let's say, I will pay a very small fee of 35,000 sats to a 40 input / 1 output transaction. This will stay unconfirmed for a longer period (maybe 1-2-3 weeks). If it stays unconfirmed, I will try to spend the unconfirmed output into another output, this time with the highest fee of a 1 input / 1 output transaction (at the time of writing this post at a 107 sats / vbyte, a total of about 15,000 sats). Will this increase my chances of being both transactions included into a block?